Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4645305 | Applied Numerical Mathematics | 2013 | 12 Pages |
The Markovian regime-switching paradigm has become one of the prevailing models in mathematical finance. It is now widely known that under the regime-switching model, the market is incomplete and so the option valuation problem in this framework will be a challenging task of considerable importance for market practitioners and academia. Our concern here is to solve the pricing problem for American options in a Markov-modulated jump-diffusion model, based on a meshfree approach using radial basis functions. In this respect, we solve a set of coupled partial integro-differential equations with the free boundary feature by expanding the solution vector in terms of radial basis functions and then collocating the resulting system of equations at some pre-specified points. This method exhibits a superlinear order of convergence in space and a linear order in time and also has an acceptable speed in comparison with some existing methods. We will compare our results with some recently proposed approaches.